Resumen de A vanishing theorem for oriented intersection multiplicities

Jean Fasel, V. Srinivas

• Let $A$ be a regular local ring containing $1/2$, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of $A$ satisfy the following property: given two elements with supports which do not intersect properly, their product vanishes. This gives an analogue for ``oriented intersection multiplicities'' of Serre's vanishing result for intersection multiplicities. It also suggests a Vanishing Conjecture for arbitrary regular local rings containing $1/2$, which is analogous to Serre's (which was proved independently by Roberts, and Gillet and Soul\'e).